The monoid of semisimple multiclasses of the group G =G2(K)

Let G be a group, and let C1,…, CK be a sequence of conjugacy classes in G. The product C1 C2 … CK = (C1C2…Ck | Ci £C1) is called a multiclass in G. Further, let G be a simple algebraic group, and let M cs(G) be the set of closures (with respect to the Zariski topology) of all multiclasses of G that are generated by semisimple conjugacy classes of G. Then M ca(G) is a monoid with respect to the operation m1 · = mim2, where rn is the closure of m. In this paper, we give a description of M cs(G) in the case of G = G2(K), where K is an algebraically closed field of characteristic zero. ©2002 Plenum Publishing Corporation.